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Discovering that all outs not the same

Playing Texas hold’em, we often speak of drawing hands and made hands. The latter could very well be in the lead and hold up to take the pot without further improvement. A pair of Aces or a set is a good example. As for a drawing hand, it usually must improve to become a made hand and (hopefully) win the pot. In that case, the unseen cards (presumed to still be in the deck) that will complete (i.e., make) that hand, are called “outs.”

Example: Drawing hands are quite common. Let’s use a typical situation to better explain the concept of “outs” and their significance. There will be many times when you find yourself holding four to a flush after the flop. Say you saw the flop with K-10 of hearts, and the flop came down Qh-8h-2d.

You now hold four to the King-high flush. You need just one more heart to complete the flush, a made hand, that would very likely (hopefully) win the pot. There are nine more hearts remaining in the deck (13 - 4). With a bit of luck, you will catch one of them on the turn or on the river. With nine outs and two cards to come, we use the 4-2 Rule to estimate the card odds.

The chance (probability) of making the flush is 4 x 9 = 36 or approximately 36 percent you will connect on the turn or on the river.

What does this mean to you? For every 100 such hands, you can expect to catch your big flush 36 times and miss 64 (100 - 36). Thus, your card odds are 64 divided by 36, which equals approximately 1.8 to 1 against connecting.

Rounding it off to 2 to 1, the pot odds need only be that amount or higher to justify calling on the turn. That gives you a Positive Expectation – pot odds higher than your card odds. In the long run, you will come out well ahead by calling an opponent’s bet to see the turn and river.

Up to this point, we have regarded all of the nine remaining hearts as being of equal value. Let’s look at a slightly different flop on the board: Qh-8h-8s. That pair of 8’s on the flop could be troublesome. Let’s suppose an opponent holds 7d-7c in the hole – pocket 7’s. Should the 7 of hearts fall on the board, it would give you your big flush, but it also gives him a full-boat – 7’s full of 8’s.

Your King-high heart flush has become a costly loser. (If this happened on the river, you could tell your poker buddies how you were rivered with a bad beat. Your opponent had only two outs at that point! Oh well, that’s poker.)

In such a case, obviously, the 7h does not deserve full value as do the other unseen hearts presumed to remain in the deck. (Poker expert Byron Ziman would label the 7h a “tainted out.”)

Of course, you have no way of knowing your opponent has pocket 7’s (or any other pocket pair). If you catch your big flush, most often it will win the pot, but it would be wise to discount one of the remaining nine hearts. In that case, instead of nine outs, assume you have one less – eight outs. And so, the pot must be about 10 percent bigger than your original estimate to warrant paying to see the turn.

In this case, recognizing the reason for that 10 percent reduction in the value of your outs could change how you play that hand, making you somewhat more cautious: Check on the river. Just think, if you had open bet on the river, your (lucky-for-him) opponent would have raised you after catching his full-house.

Of course, you might hesitate, but ultimately you call his raise – and lose a big pot.